Why do astronauts feel weightlessness?

They feel weightless because they are indeed weightless when in orbit, in effect in freefall. Gravity tries to pull them down but the spacecraft motion carries it "past the planet" in an arc that is part of a circular or elliptical orbit. If the spacecraft slows down, it will be pulled toward the Earth by the considerable gravitational force.

If an astronaut tries to use an ordinary scale to measure her weight, all attempts will be useless. The vessel she is in is under the influence of Earth's gravity, it is true, as is her body. But the vessel and her body are in the same orbit, at the same velocity. If she is motionless at the center of the vessel, no unbalanced forces will push her "down" toward the floor or hull of the vessel. And if there are some unbalanced forces, they are so small as to be negligible for all practical purposes. She will not be able to 'step' onto a scale, unless she is in some kind of rotating vessel, which would provide a kind of artificial gravity.